In this work, we report the set-up and results of the Liver Tumor Segmentation Benchmark (LiTS), which was organized in conjunction with the IEEE International Symposium on Biomedical Imaging (ISBI) 2017 and the International Conferences on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2017 and 2018. The image dataset is diverse and contains primary and secondary tumors with varied sizes and appearances with various lesion-to-background levels (hyper-/hypo-dense), created in collaboration with seven hospitals and research institutions. Seventy-five submitted liver and liver tumor segmentation algorithms were trained on a set of 131 computed tomography (CT) volumes and were tested on 70 unseen test images acquired from different patients. We found that not a single algorithm performed best for both liver and liver tumors in the three events. The best liver segmentation algorithm achieved a Dice score of 0.963, whereas, for tumor segmentation, the best algorithms achieved Dices scores of 0.674 (ISBI 2017), 0.702 (MICCAI 2017), and 0.739 (MICCAI 2018). Retrospectively, we performed additional analysis on liver tumor detection and revealed that not all top-performing segmentation algorithms worked well for tumor detection. The best liver tumor detection method achieved a lesion-wise recall of 0.458 (ISBI 2017), 0.515 (MICCAI 2017), and 0.554 (MICCAI 2018), indicating the need for further research. LiTS remains an active benchmark and resource for research, e.g., contributing the liver-related segmentation tasks in http://medicaldecathlon.com/. In addition, both data and online evaluation are accessible via https://competitions.codalab.org/competitions/17094.

Lineage tracing, the joint segmentation and tracking of living cells as they move and divide in a sequence of light microscopy images, is a challenging task. Jug et al. [21] have proposed a mathematical abstraction of this task, the moral lineage tracing problem (MLTP), whose feasible solutions define both a segmentation of every image and a lineage forest of cells. Their branch-and-cut algorithm, however, is prone to many cuts and slow convergence for large instances. To address this problem, we make three contributions: (i) we devise the first efficient primal feasible local search algorithms for the MLTP, (ii) we improve the branch-and-cut algorithm by separating tighter cutting planes and by incorporating our primal algorithms, (iii) we show in experiments that our algorithms find accurate solutions on the problem instances of Jug et al. and scale to larger instances, leveraging moral lineage tracing to practical significance.

Several important tasks in medical image analysis can be stated in the form of an optimization problem whose feasible solutions are connected subgraphs. Examples include the reconstruction of neural or vascular structures under connectedness constraints. We discuss the minimum cost connected subgraph (MCCS) problem and its approximations from the perspective of medical applications. We propose (a) objective-dependent constraints and (b) novel constraint generation schemes to solve this optimization problem exactly by means of a branch-and-cut algorithm. These are shown to improve scalability and allow us to solve instances of two medical benchmark datasets to optimality for the first time. This enables us to perform a quantitative comparison between exact and approximative algorithms, where we identify the geodesic tree algorithm as an excellent alternative to exact inference on the examined datasets. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.